Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
394 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11711655 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11711537 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | A4×#508 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #152161 | — | 3 | 1 | no | maximal, Sylow |
| 5 | A4×#135 | — | 2 | 1 | no | — |
| 6 | A4×Q32 | C4 | 1 | 1 | yes | characteristic, complemented |
| 7 | A4×SD32 | — | 2 | 1 | no | — |
| 8 | A4×D16 | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | C2×A4×C16 | C22 | 1 | 1 | yes | characteristic |
| 10 | #73111 | — | 2 | 1 | no | — |
| 11 | A4⋊C32 | — | 2 | 1 | no | — |
| 12 | #67828 | — | 4 | 1 | no | maximal |
| 13 | C22×#508 | D3 | 1 | 1 | yes | characteristic |
| 14 | C2×#1418 | — | 3 | 1 | no | — |
| 15 | C2×#1418 | — | 3 | 1 | no | — |
| 16 | C2×#1418 | — | 3 | 1 | no | — |
| 17 | C2×#1418 | — | 3 | 1 | no | — |
| 18 | #13553 | — | 3 | 1 | no | — |
| 19 | #12835 | — | 3 | 1 | no | — |
| 20 | A4×#41 | — | 4 | 1 | no | — |
| 21 | A4×Q16 | — | 2 | 1 | no | — |
| 22 | A4×SD16 | — | 4 | 1 | no | — |
| 23 | A4×D8 | — | 2 | 1 | no | — |
| 24 | C2×C8×A4 | D4 | 1 | 1 | yes | characteristic |
| 25 | C4⋊SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 26 | C3×#508 | — | 4 | 1 | no | — |
| 27 | A4×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 28 | A4×C16 | D4 | 1 | 1 | yes | characteristic |
| 29 | #4505 | — | 4 | 1 | no | — |
| 30 | #4499 | — | 4 | 1 | no | — |
| 31 | C22×#135 | — | 2 | 1 | no | — |
| 32 | C2×#508 | — | 3 | 1 | no | — |
| 33 | C2×#508 | — | 3 | 1 | no | — |
| 34 | C2×#508 | — | 3 | 1 | no | — |
| 35 | C2×#508 | — | 3 | 1 | no | — |
| 36 | C2×#508 | — | 6 | 1 | no | — |
| 37 | C2×#508 | — | 6 | 1 | no | — |
| 38 | C22×Q32 | Dic3 | 1 | 1 | yes | characteristic, complemented |
| 39 | C22×SD32 | — | 2 | 1 | no | — |
| 40 | C22×D16 | Dic3 | 1 | 1 | yes | characteristic, complemented |
| 41 | C23×C16 | C2×D3 | 1 | 1 | yes | characteristic |
| 42 | C2×M64 | — | 3 | 1 | no | — |
| 43 | C2×M64 | — | 3 | 1 | no | — |
| 44 | C2×#367 | — | 3 | 1 | no | — |
| 45 | C2×#367 | — | 3 | 1 | no | — |
| 46 | #1808 | — | 6 | 1 | no | — |
| 47 | #1418 | — | 6 | 2 | no | — |
| 48 | #1418 | — | 6 | 2 | no | — |
| 49 | #1418 | — | 6 | 1 | no | — |
| 50 | #1418 | — | 6 | 1 | no | — |
| 51 | #1418 | — | 6 | 1 | no | — |
| 52 | #1418 | — | 6 | 1 | no | — |
| 53 | C22⋊C32 | — | 6 | 1 | no | — |
| 54 | C22⋊C32 | — | 6 | 1 | no | — |
| 55 | #1380 | — | 6 | 1 | no | — |
| 56 | Q8×A4 | — | 4 | 1 | no | — |
| 57 | D4×A4 | — | 4 | 1 | no | — |
| 58 | D4×A4 | — | 8 | 1 | no | — |
| 59 | C2×C4×A4 | — | 8 | 1 | no | — |
| 60 | C2×C4×A4 | D8 | 1 | 1 | yes | characteristic |
| 61 | C2×SL(2,ℤ/4) | — | 8 | 1 | no | — |
| 62 | C3×#135 | — | 8 | 1 | no | — |
| 63 | C8×A4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 64 | C8×A4 | SD16 | 1 | 1 | yes | characteristic |
| 65 | C3×Q32 | — | 4 | 1 | no | — |
| 66 | C3×SD32 | — | 8 | 1 | no | — |
| 67 | C3×D16 | — | 4 | 1 | no | — |
| 68 | C2×C3×C16 | — | 4 | 1 | no | — |
| 69 | #818 | — | 8 | 1 | no | — |
| 70 | C3⋊C32 | — | 8 | 1 | no | — |
| 71 | C22×#41 | — | 4 | 1 | no | — |
| 72 | C2×#135 | — | 6 | 1 | no | — |
| 73 | C2×#135 | — | 6 | 1 | no | — |
| 74 | C2×#135 | — | 6 | 1 | no | — |
| 75 | C2×#135 | — | 6 | 1 | no | — |
| 76 | C2×#135 | — | 12 | 1 | no | — |
| 77 | C2×#135 | — | 12 | 1 | no | — |
| 78 | C22×Q16 | — | 2 | 1 | no | — |
| 79 | C22×SD16 | — | 4 | 1 | no | — |
| 80 | C22×D8 | — | 2 | 1 | no | — |
| 81 | C23×C8 | #67 | 1 | 1 | yes | characteristic |
| 82 | #508 | — | 3 | 2 | no | — |
| 83 | #508 | — | 3 | 2 | no | — |
| 84 | #508 | — | 3 | 1 | no | — |
| 85 | #508 | — | 3 | 1 | no | — |
| 86 | #508 | — | 3 | 1 | no | — |
| 87 | #508 | — | 6 | 1 | no | — |
| 88 | #508 | — | 6 | 1 | no | — |
| 89 | #508 | — | 6 | 1 | no | — |
| 90 | #508 | — | 6 | 2 | no | — |
| 91 | #508 | — | 6 | 2 | no | — |
| 92 | #508 | S4 | 1 | 1 | yes | characteristic |
| 93 | C2×Q32 | — | 3 | 1 | no | — |
| 94 | C2×Q32 | — | 3 | 1 | no | — |
| 95 | C2×Q32 | — | 6 | 1 | no | — |
| 96 | C2×SD32 | — | 6 | 1 | no | — |
| 97 | C2×SD32 | — | 6 | 1 | no | — |
| 98 | C2×SD32 | — | 6 | 1 | no | — |
| 99 | C2×SD32 | — | 6 | 1 | no | — |
| 100 | C2×D16 | — | 3 | 1 | no | — |
| 101 | C2×D16 | — | 3 | 1 | no | — |
| 102 | C2×D16 | — | 6 | 1 | no | — |
| 103 | C22×C16 | — | 3 | 1 | no | — |
| 104 | C22×C16 | — | 3 | 1 | no | — |
| 105 | C22×C16 | — | 3 | 1 | no | — |
| 106 | C22×C16 | — | 3 | 1 | no | — |
| 107 | C22×C16 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 108 | C22×C16 | #67 | 1 | 1 | yes | characteristic |
| 109 | C2×#107 | — | 6 | 1 | no | — |
| 110 | C2×#107 | — | 6 | 1 | no | — |
| 111 | #380 | — | 12 | 1 | no | — |
| 112 | M64 | — | 6 | 1 | no | — |
| 113 | M64 | — | 6 | 1 | no | — |
| 114 | M64 | — | 6 | 1 | no | — |
| 115 | M64 | — | 6 | 1 | no | — |
| 116 | C2×C32 | — | 6 | 1 | no | — |
| 117 | C2×C32 | — | 6 | 1 | no | — |
| 118 | #367 | — | 6 | 1 | no | — |
| 119 | #367 | — | 6 | 1 | no | — |
| 120 | #367 | — | 6 | 1 | no | — |
| 121 | #367 | — | 6 | 1 | no | — |
| 122 | #340 | — | 12 | 1 | no | — |
| 123 | C22×A4 | — | 8 | 1 | no | — |
| 124 | C22×A4 | D16 | 1 | 1 | yes | characteristic |
| 125 | C3×#41 | — | 16 | 1 | no | — |
| 126 | C4×A4 | — | 8 | 1 | no | — |
| 127 | C4×A4 | #102 | 1 | 1 | yes | characteristic |
| 128 | C4×A4 | SD32 | 1 | 1 | yes | characteristic |
| 129 | SL(2,ℤ/4) | — | 16 | 1 | no | — |
| 130 | C3×Q16 | — | 8 | 1 | no | — |
| 131 | C3×SD16 | — | 16 | 1 | no | — |
| 132 | C3×D8 | — | 8 | 1 | no | — |
| 133 | C2×C3×C8 | — | 4 | 1 | no | — |
| 134 | C4⋊Dic3 | — | 16 | 1 | no | — |
| 135 | C3×C16 | — | 4 | 1 | no | — |
| 136 | C3×C16 | — | 4 | 1 | no | — |
| 137 | C2×#41 | — | 12 | 1 | no | — |
| 138 | C2×#41 | — | 12 | 1 | no | — |
| 139 | C2×#41 | — | 12 | 1 | no | — |
| 140 | C2×#41 | — | 12 | 1 | no | — |
| 141 | C2×#41 | — | 24 | 1 | no | — |
| 142 | C2×#41 | — | 24 | 1 | no | — |
| 143 | C22×Q8 | — | 4 | 1 | no | — |
| 144 | C22×D4 | — | 4 | 1 | no | — |
| 145 | C22×D4 | — | 8 | 1 | no | — |
| 146 | C23×C4 | — | 8 | 1 | no | — |
| 147 | C23×C4 | #213 | 1 | 1 | yes | characteristic |
| 148 | #135 | — | 2 | 1 | no | — |
| 149 | #135 | — | 6 | 1 | no | — |
| 150 | #135 | — | 6 | 1 | no | — |
| 151 | #135 | — | 6 | 2 | no | — |
| 152 | #135 | — | 6 | 1 | no | — |
| 153 | #135 | — | 12 | 1 | no | — |
| 154 | #135 | — | 12 | 1 | no | — |
| 155 | #135 | — | 12 | 1 | no | — |
| 156 | #135 | — | 12 | 1 | no | — |
| 157 | #135 | — | 12 | 2 | no | — |
| 158 | #135 | — | 12 | 2 | no | — |
| 159 | C2×Q16 | — | 6 | 1 | no | — |
| 160 | C2×Q16 | — | 6 | 1 | no | — |
| 161 | C2×Q16 | — | 12 | 1 | no | — |
| 162 | C2×SD16 | — | 12 | 1 | no | — |
| 163 | C2×SD16 | — | 12 | 1 | no | — |
| 164 | C2×SD16 | — | 12 | 1 | no | — |
| 165 | C2×SD16 | — | 12 | 1 | no | — |
| 166 | C2×D8 | — | 6 | 1 | no | — |
| 167 | C2×D8 | — | 6 | 1 | no | — |
| 168 | C2×D8 | — | 12 | 1 | no | — |
| 169 | C22×C8 | — | 3 | 1 | no | — |
| 170 | C22×C8 | — | 3 | 1 | no | — |
| 171 | C22×C8 | — | 3 | 1 | no | — |
| 172 | C22×C8 | — | 3 | 1 | no | — |
| 173 | C22×C8 | #214 | 1 | 1 | yes | characteristic |
| 174 | C22×C8 | #217 | 1 | 1 | yes | characteristic |
| 175 | C2×C4⋊C4 | — | 12 | 1 | no | — |
| 176 | C2×C4⋊C4 | — | 12 | 1 | no | — |
| 177 | C2×C22⋊C4 | — | 24 | 1 | no | — |
| 178 | Q32 | — | 3 | 2 | no | — |
| 179 | Q32 | — | 3 | 1 | no | — |
| 180 | Q32 | — | 6 | 1 | no | — |
| 181 | Q32 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic, complemented |
| 182 | SD32 | — | 2 | 1 | no | — |
| 183 | SD32 | — | 6 | 1 | no | — |
| 184 | SD32 | — | 6 | 1 | no | — |
| 185 | SD32 | — | 6 | 2 | no | — |
| 186 | SD32 | — | 6 | 1 | no | — |
| 187 | D16 | — | 3 | 2 | no | — |
| 188 | D16 | — | 3 | 1 | no | — |
| 189 | D16 | — | 6 | 1 | no | — |
| 190 | D16 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic, complemented |
| 191 | C2×C16 | — | 3 | 1 | no | — |
| 192 | C2×C16 | — | 3 | 1 | no | — |
| 193 | C2×C16 | — | 3 | 1 | no | — |
| 194 | C2×C16 | — | 3 | 1 | no | — |
| 195 | C2×C16 | — | 3 | 1 | no | — |
| 196 | C2×C16 | — | 3 | 1 | no | — |
| 197 | C2×C16 | — | 3 | 1 | no | — |
| 198 | C2×C16 | — | 6 | 1 | no | — |
| 199 | C2×C16 | C2×S4 | 1 | 1 | yes | characteristic |
| 200 | #107 | — | 12 | 1 | no | — |
| 201 | #107 | — | 12 | 1 | no | — |
| 202 | #107 | — | 12 | 1 | no | — |
| 203 | #107 | — | 12 | 1 | no | — |
| 204 | #95 | — | 24 | 1 | no | — |
| 205 | C32 | — | 12 | 1 | no | — |
| 206 | C32 | — | 12 | 1 | no | — |
| 207 | C2×A4 | — | 2 | 1 | no | — |
| 208 | C2×A4 | — | 16 | 1 | no | — |
| 209 | C2×A4 | #357 | 1 | 1 | yes | characteristic |
| 210 | C3×Q8 | — | 16 | 1 | no | — |
| 211 | C3×D4 | — | 16 | 1 | no | — |
| 212 | C3×D4 | — | 32 | 1 | no | — |
| 213 | C2×C3×C4 | — | 4 | 1 | no | — |
| 214 | C2×C3×C4 | — | 32 | 1 | no | — |
| 215 | C2×Dic3 | — | 32 | 1 | no | — |
| 216 | C3×C8 | — | 4 | 1 | no | — |
| 217 | C3×C8 | — | 4 | 1 | no | — |
| 218 | C24 | — | 8 | 1 | no | — |
| 219 | C24 | #826 | 1 | 1 | yes | characteristic |
| 220 | #41 | — | 4 | 1 | no | — |
| 221 | #41 | — | 12 | 1 | no | — |
| 222 | #41 | — | 12 | 1 | no | — |
| 223 | #41 | — | 12 | 2 | no | — |
| 224 | #41 | — | 12 | 1 | no | — |
| 225 | #41 | — | 24 | 1 | no | — |
| 226 | #41 | — | 24 | 1 | no | — |
| 227 | #41 | — | 24 | 1 | no | — |
| 228 | #41 | — | 24 | 1 | no | — |
| 229 | #41 | — | 24 | 2 | no | — |
| 230 | #41 | — | 24 | 2 | no | — |
| 231 | C2×Q8 | — | 12 | 1 | no | — |
| 232 | C2×Q8 | — | 12 | 1 | no | — |
| 233 | C2×Q8 | — | 24 | 1 | no | — |
| 234 | C2×D4 | — | 12 | 1 | no | — |
| 235 | C2×D4 | — | 12 | 1 | no | — |
| 236 | C2×D4 | — | 24 | 1 | no | — |
| 237 | C2×D4 | — | 24 | 1 | no | — |
| 238 | C2×D4 | — | 24 | 1 | no | — |
| 239 | C2×D4 | — | 24 | 1 | no | — |
| 240 | C2×D4 | — | 24 | 1 | no | — |
| 241 | C22×C4 | — | 3 | 1 | no | — |
| 242 | C22×C4 | — | 3 | 1 | no | — |
| 243 | C22×C4 | — | 3 | 1 | no | — |
| 244 | C22×C4 | — | 3 | 1 | no | — |
| 245 | C22×C4 | — | 8 | 1 | no | — |
| 246 | C22×C4 | — | 24 | 1 | no | — |
| 247 | C22×C4 | — | 24 | 1 | no | — |
| 248 | C22×C4 | — | 24 | 1 | no | — |
| 249 | C22×C4 | — | 24 | 1 | no | — |
| 250 | C22×C4 | — | 24 | 1 | no | — |
| 251 | C22×C4 | — | 24 | 1 | no | — |
| 252 | C22×C4 | #827 | 1 | 1 | yes | characteristic |
| 253 | C22×C4 | #832 | 1 | 1 | yes | characteristic |
| 254 | Q16 | — | 2 | 1 | no | — |
| 255 | Q16 | — | 6 | 1 | no | — |
| 256 | Q16 | — | 12 | 1 | no | — |
| 257 | Q16 | — | 12 | 1 | no | — |
| 258 | SD16 | — | 4 | 1 | no | — |
| 259 | SD16 | — | 12 | 1 | no | — |
| 260 | SD16 | — | 12 | 1 | no | — |
| 261 | SD16 | — | 12 | 2 | no | — |
| 262 | SD16 | — | 12 | 1 | no | — |
| 263 | D8 | — | 2 | 1 | no | — |
| 264 | D8 | — | 6 | 1 | no | — |
| 265 | D8 | — | 12 | 1 | no | — |
| 266 | D8 | — | 12 | 1 | no | — |
| 267 | C2×C8 | — | 3 | 1 | no | — |
| 268 | C2×C8 | — | 3 | 1 | no | — |
| 269 | C2×C8 | — | 3 | 1 | no | — |
| 270 | C2×C8 | — | 3 | 1 | no | — |
| 271 | C2×C8 | — | 3 | 1 | no | — |
| 272 | C2×C8 | — | 3 | 1 | no | — |
| 273 | C2×C8 | — | 3 | 1 | no | — |
| 274 | C2×C8 | — | 6 | 1 | no | — |
| 275 | C2×C8 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 276 | C4⋊C4 | — | 24 | 1 | no | — |
| 277 | C4⋊C4 | — | 24 | 1 | no | — |
| 278 | C4⋊C4 | — | 24 | 1 | no | — |
| 279 | C4⋊C4 | — | 24 | 1 | no | — |
| 280 | C22⋊C4 | — | 48 | 1 | no | — |
| 281 | C22⋊C4 | — | 48 | 1 | no | — |
| 282 | C16 | — | 3 | 1 | no | — |
| 283 | C16 | — | 3 | 1 | no | — |
| 284 | C16 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 285 | C16 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 286 | C22×C3 | — | 4 | 1 | no | — |
| 287 | C22×C3 | — | 32 | 1 | no | — |
| 288 | A4 | #1418 | 1 | 1 | yes | characteristic, complemented |
| 289 | C3×C4 | — | 4 | 1 | no | — |
| 290 | C3×C4 | — | 4 | 1 | no | — |
| 291 | C3×C4 | — | 32 | 1 | no | — |
| 292 | Dic3 | — | 64 | 1 | no | — |
| 293 | C23 | — | 2 | 1 | no | — |
| 294 | C23 | — | 3 | 1 | no | — |
| 295 | C23 | — | 3 | 1 | no | — |
| 296 | C23 | — | 6 | 1 | no | — |
| 297 | C23 | — | 16 | 1 | no | — |
| 298 | C23 | — | 24 | 1 | no | — |
| 299 | C23 | — | 24 | 1 | no | — |
| 300 | C23 | — | 48 | 1 | no | — |
| 301 | C23 | #4562 | 1 | 1 | yes | characteristic |
| 302 | Q8 | — | 4 | 1 | no | — |
| 303 | Q8 | — | 12 | 1 | no | — |
| 304 | Q8 | — | 24 | 1 | no | — |
| 305 | Q8 | — | 24 | 1 | no | — |
| 306 | D4 | — | 4 | 1 | no | — |
| 307 | D4 | — | 8 | 1 | no | — |
| 308 | D4 | — | 12 | 1 | no | — |
| 309 | D4 | — | 24 | 1 | no | — |
| 310 | D4 | — | 24 | 1 | no | — |
| 311 | D4 | — | 24 | 1 | no | — |
| 312 | D4 | — | 24 | 1 | no | — |
| 313 | D4 | — | 24 | 2 | no | — |
| 314 | D4 | — | 24 | 1 | no | — |
| 315 | C2×C4 | — | 3 | 1 | no | — |
| 316 | C2×C4 | — | 3 | 1 | no | — |
| 317 | C2×C4 | — | 3 | 1 | no | — |
| 318 | C2×C4 | — | 3 | 1 | no | — |
| 319 | C2×C4 | — | 3 | 1 | no | — |
| 320 | C2×C4 | — | 3 | 1 | no | — |
| 321 | C2×C4 | — | 3 | 1 | no | — |
| 322 | C2×C4 | — | 6 | 1 | no | — |
| 323 | C2×C4 | — | 8 | 1 | no | — |
| 324 | C2×C4 | — | 24 | 1 | no | — |
| 325 | C2×C4 | — | 24 | 1 | no | — |
| 326 | C2×C4 | — | 24 | 2 | no | — |
| 327 | C2×C4 | — | 24 | 1 | no | — |
| 328 | C2×C4 | — | 24 | 1 | no | — |
| 329 | C2×C4 | — | 24 | 1 | no | — |
| 330 | C2×C4 | — | 48 | 1 | no | — |
| 331 | C2×C4 | — | 48 | 1 | no | — |
| 332 | C2×C4 | — | 48 | 1 | no | — |
| 333 | C2×C4 | — | 48 | 1 | no | — |
| 334 | C2×C4 | — | 48 | 1 | no | — |
| 335 | C2×C4 | — | 48 | 1 | no | — |
| 336 | C2×C4 | #5415 | 1 | 1 | yes | characteristic |
| 337 | C8 | — | 3 | 1 | no | — |
| 338 | C8 | — | 3 | 1 | no | — |
| 339 | C8 | #5414 | 1 | 1 | yes | characteristic |
| 340 | C8 | #5432 | 1 | 1 | yes | characteristic |
| 341 | C2×C3 | — | 4 | 1 | no | — |
| 342 | C2×C3 | — | 8 | 1 | no | — |
| 343 | C2×C3 | — | 64 | 1 | no | — |
| 344 | C22 | — | 3 | 1 | no | — |
| 345 | C22 | — | 3 | 1 | no | — |
| 346 | C22 | — | 3 | 1 | no | — |
| 347 | C22 | — | 6 | 1 | no | — |
| 348 | C22 | — | 6 | 1 | no | — |
| 349 | C22 | — | 6 | 1 | no | — |
| 350 | C22 | — | 6 | 1 | no | — |
| 351 | C22 | — | 8 | 1 | no | — |
| 352 | C22 | — | 24 | 1 | no | — |
| 353 | C22 | — | 48 | 1 | no | — |
| 354 | C22 | — | 48 | 1 | no | — |
| 355 | C22 | — | 48 | 1 | no | — |
| 356 | C22 | — | 48 | 1 | no | — |
| 357 | C22 | #67828 | 1 | 1 | yes | characteristic, complemented |
| 358 | C22 | #73133 | 1 | 1 | yes | characteristic |
| 359 | C4 | — | 3 | 1 | no | — |
| 360 | C4 | — | 3 | 1 | no | — |
| 361 | C4 | — | 8 | 1 | no | — |
| 362 | C4 | — | 24 | 1 | no | — |
| 363 | C4 | — | 96 | 1 | no | — |
| 364 | C4 | — | 96 | 1 | no | — |
| 365 | C4 | #73134 | 1 | 1 | yes | characteristic |
| 366 | C4 | #73144 | 1 | 1 | yes | characteristic |
| 367 | C3 | — | 4 | 1 | no | Sylow |
| 368 | C2 | — | 2 | 1 | no | — |
| 369 | C2 | — | 3 | 1 | no | — |
| 370 | C2 | — | 3 | 1 | no | — |
| 371 | C2 | — | 6 | 1 | no | — |
| 372 | C2 | — | 16 | 1 | no | — |
| 373 | C2 | — | 48 | 1 | no | — |
| 374 | C2 | #11711514 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11711655 | C2 | semidirect |
| 2. #11711537 | C2 | semidirect |
| 6. A4×Q32 | C4 | semidirect |
| 8. A4×D16 | C4 | semidirect |
| 38. C22×Q32 | Dic3 | semidirect |
| 40. C22×D16 | Dic3 | semidirect |
| 181. Q32 | SL(2,ℤ/4) | semidirect |
| 190. D16 | SL(2,ℤ/4) | semidirect |
| 288. A4 | #1418 | semidirect |
| 357. C22 | #67828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11711655 | 2 |
| #11711537 | 2 |
| A4×#508 | 2 |
| #152161 | 3 |
| #67828 | 4 |